They don’t bother with Chicago because it has no political benefit. Chicago has some of the strictest guns laws in the US. They don’t want to showcase the failure that the more controlling laws are.
http://topics.nytimes.com/top/reference/timestopics/subjects/g/gun_control/index.html
Besides, if they lowered the flags every time someone was killed in Chicago, they'd never fly at the top of the pole again.